pcg32.h

/*
 * Tiny self-contained version of the PCG Random Number Generation for C++
 * put together from pieces of the much larger C/C++ codebase.
 * Wenzel Jakob, February 2015
 *
 * The PCG random number generator was developed by Melissa O'Neill
 * <oneill@pcg-random.org>
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 *
 * For additional information about the PCG random number generation scheme,
 * including its license and other licensing options, visit
 *
 *     http://www.pcg-random.org
 */

#ifndef __PCG32_H
#define __PCG32_H 1

#define PCG32_DEFAULT_STATE  0x853c49e6748fea9bULL
#define PCG32_DEFAULT_STREAM 0xda3e39cb94b95bdbULL
#define PCG32_MULT           0x5851f42d4c957f2dULL

#include <inttypes.h>
#include <cmath>
#include <cassert>
#include <algorithm>

/// PCG32 Pseudorandom number generator
struct pcg32 {
    /// Initialize the pseudorandom number generator with default seed
    pcg32() : state(PCG32_DEFAULT_STATE), inc(PCG32_DEFAULT_STREAM) {}

    /// Initialize the pseudorandom number generator with the \ref seed() function
    pcg32(uint64_t initstate, uint64_t initseq = 1u) { seed(initstate, initseq); }

    /**
     * \brief Seed the pseudorandom number generator
     *
     * Specified in two parts: a state initializer and a sequence selection
     * constant (a.k.a. stream id)
     */
    void seed(uint64_t initstate, uint64_t initseq = 1) {
        state = 0U;
        inc = (initseq << 1u) | 1u;
        nextUInt();
        state += initstate;
        nextUInt();
    }

    /// Generate a uniformly distributed unsigned 32-bit random number
    uint32_t nextUInt() {
        uint64_t oldstate = state;
        state = oldstate * PCG32_MULT + inc;
        uint32_t xorshifted = (uint32_t) (((oldstate >> 18u) ^ oldstate) >> 27u);
        uint32_t rot = (uint32_t) (oldstate >> 59u);
        return (xorshifted >> rot) | (xorshifted << ((~rot + 1u) & 31));
    }

    /// Generate a uniformly distributed number, r, where 0 <= r < bound
    uint32_t nextUInt(uint32_t bound) {
        // To avoid bias, we need to make the range of the RNG a multiple of
        // bound, which we do by dropping output less than a threshold.
        // A naive scheme to calculate the threshold would be to do
        //
        //     uint32_t threshold = 0x100000000ull % bound;
        //
        // but 64-bit div/mod is slower than 32-bit div/mod (especially on
        // 32-bit platforms).  In essence, we do
        //
        //     uint32_t threshold = (0x100000000ull-bound) % bound;
        //
        // because this version will calculate the same modulus, but the LHS
        // value is less than 2^32.

        uint32_t threshold = (~bound+1u) % bound;

        // Uniformity guarantees that this loop will terminate.  In practice, it
        // should usually terminate quickly; on average (assuming all bounds are
        // equally likely), 82.25% of the time, we can expect it to require just
        // one iteration.  In the worst case, someone passes a bound of 2^31 + 1
        // (i.e., 2147483649), which invalidates almost 50% of the range.  In
        // practice, bounds are typically small and only a tiny amount of the range
        // is eliminated.
        for (;;) {
            uint32_t r = nextUInt();
            if (r >= threshold)
                return r % bound;
        }
    }

    /// Generate a single precision floating point value on the interval [0, 1)
    float nextFloat() {
        /* Trick from MTGP: generate an uniformly distributed
           single precision number in [1,2) and subtract 1. */
        union {
            uint32_t u;
            float f;
        } x;
        x.u = (nextUInt() >> 9) | 0x3f800000u;
        return x.f - 1.0f;
    }

    /**
     * \brief Generate a double precision floating point value on the interval [0, 1)
     *
     * \remark Since the underlying random number generator produces 32 bit output,
     * only the first 32 mantissa bits will be filled (however, the resolution is still
     * finer than in \ref nextFloat(), which only uses 23 mantissa bits)
     */
    double nextDouble() {
        /* Trick from MTGP: generate an uniformly distributed
           double precision number in [1,2) and subtract 1. */
        union {
            uint64_t u;
            double d;
        } x;
        x.u = ((uint64_t) nextUInt() << 20) | 0x3ff0000000000000ULL;
        return x.d - 1.0;
    }

    /**
     * \brief Multi-step advance function (jump-ahead, jump-back)
     *
     * The method used here is based on Brown, "Random Number Generation
     * with Arbitrary Stride", Transactions of the American Nuclear
     * Society (Nov. 1994). The algorithm is very similar to fast
     * exponentiation.
     */
    void advance(int64_t delta_) {
        uint64_t
            cur_mult = PCG32_MULT,
            cur_plus = inc,
            acc_mult = 1u,
            acc_plus = 0u;

        /* Even though delta is an unsigned integer, we can pass a signed
           integer to go backwards, it just goes "the long way round". */
        uint64_t delta = (uint64_t) delta_;

        while (delta > 0) {
            if (delta & 1) {
                acc_mult *= cur_mult;
                acc_plus = acc_plus * cur_mult + cur_plus;
            }
            cur_plus = (cur_mult + 1) * cur_plus;
            cur_mult *= cur_mult;
            delta /= 2;
        }
        state = acc_mult * state + acc_plus;
    }

    /**
     * \brief Draw uniformly distributed permutation and permute the
     * given STL container
     *
     * From: Knuth, TAoCP Vol. 2 (3rd 3d), Section 3.4.2
     */
    template <typename Iterator> void shuffle(Iterator begin, Iterator end) {
        for (Iterator it = end - 1; it > begin; --it)
            std::iter_swap(it, begin + nextUInt((uint32_t) (it - begin + 1)));
    }

    /// Compute the distance between two PCG32 pseudorandom number generators
    int64_t operator-(const pcg32 &other) const {
        assert(inc == other.inc);

        uint64_t
            cur_mult = PCG32_MULT,
            cur_plus = inc,
            cur_state = other.state,
            the_bit = 1u,
            distance = 0u;

        while (state != cur_state) {
            if ((state & the_bit) != (cur_state & the_bit)) {
                cur_state = cur_state * cur_mult + cur_plus;
                distance |= the_bit;
            }
            assert((state & the_bit) == (cur_state & the_bit));
            the_bit <<= 1;
            cur_plus = (cur_mult + 1ULL) * cur_plus;
            cur_mult *= cur_mult;
        }

        return (int64_t) distance;
    }

    /// Equality operator
    bool operator==(const pcg32 &other) const { return state == other.state && inc == other.inc; }

    /// Inequality operator
    bool operator!=(const pcg32 &other) const { return state != other.state || inc != other.inc; }

    uint64_t state;  // RNG state.  All values are possible.
    uint64_t inc;    // Controls which RNG sequence (stream) is selected. Must *always* be odd.
};

#endif // __PCG32_H